# MECHANICS OF SOLIDS AND STRUCTURES

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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- ELENA BENVENUTI
- Credits
- 12
- Didactic period
- Primo Semestre
- SSD
- ICAR/08

#### Training objectives

- The purpose of the course of "Scienza delle Costruzioni" (Structural analysis and strength of materials) is to provide the fundamentals of statics and kinematics of deformable solids and structures to the students of Bachelor in Civil Engineering. In particular, structures made of beams and beam systems are dealt with. The aim is to give to students the means to verify the structures subjected to assigned loads and geometry. The course aims at enabling the student to draw diagrams of the internal actions and evaluate the displacement in a given section and the state of stress at a generic section assuming a linear elastic material. A further objective is to provide the elements necessary for the design of real structures that will be faced in the course of "Tecnica delle Costruzioni" (Structural Engineering).
#### Prerequisites

- To be able to attend the course with profit, the students must have understood the contents of the courses of Calculus I and II, Geometry, Physics I and Rational Mechanics.
#### Course programme

- The main topics covered are:

1. The solution of isostatic structures (27 hours)

2. The solution of hyperstatic structures using the method of the principle of virtual work (27 hours)

3. Introduction to matrix analysis (2 h)

5. Continuum strain analysis (2 h)

6. Constitutive equations for linear-elastic continua (5 h)

7. The principle of virtual power (3 h)

8. The Minimum principle of total potential energy (1 h)

9. The problem of de Saint Venant (22 h)

10. Jourawaky's formula (2 h)

11. The verification of beam sections (3 h)

12. The strength criteria for solid materials (2 h)

13. The stability of equilibrium for beams (6 h)

14. The elastica (3 h)

The number of hours per each topic may change according to the necessity of the attendants. #### Didactic methods

- The course consists of classroom lectures and exercises that may require the involvement of the student. Tutoring activities are foreseen, consisting of weekly meetings, additional exercises outside the official class lessons.

The exam is passed after attaining a positive evaluation in the script and oral examination. The script examination can be replaced by two partial script examinations (middle November and December) during or immediately after the end of the course.

The teacher fixes weekly office hours for students needing clarifications about the topics covered during the lessons. Additional appointments can be made through email. #### Learning assessment procedures

- The exam is composed of a written test (which can be done during the course) and an oral examination.

The written test can consist either of four partial tests or of one global test.

The partial tests are specified as follows:

1) Two tests to be held in November and December regarding the solution of isostatic structures and frames;

2) two tests to be held in April and May focusing on the solution of hyperstatic structures. The minimum mark that allow admission to the oral exam is 16. For marks of 16 and 17, the student must solve a test on a hyperstatic frame during the oral exam.

The grade of the written test is the maximum between the mark obtained from the partial tests and those obtained during the global written tests.

The mark of the partial tests is the arithmetic average of the grades obtained during the tests, for instance i V1, V2, V3, V4 are the marks obtained in the four partial tests, the final mark is (V1+V2+V3+V4)/4.

The validity of the marks obtained in the partial tests extends over the academic year of reference.

The oral examination covers the following topics: The analysis of the stress, the strain of a continuum, the constitutive equations of linear-elastic continua, the problem of de Saint Venant, the strength criteria for solid materials, the stability of equilibrium for beams. #### Reference texts

- Besides the classroom handouts, the student can use the textbook:

"Scienza delle Costruzioni" by L. Nunziante, L. Gambarotta, A. Tralli, McGraw-Hill, 3° edizione 2011.